Thermal Casimir effect in Gödel-type universes

Abstract

In this paper, a massless scalar field coupled to gravity is considered. Then the Casimir effect at finite temperature is calculated. Such development is carried out in the Thermo Field Dynamics formalism. This approach presents a topological structure that allows for investigating the effects of temperature and the size effect in a similar way. These effects are calculated considering Gödel-type solutions as a gravitational background. The Stefan-Boltzmann law and its consistency are analyzed for both causal and non-causal Gödel-type regions. In this space-time and for any region, the Casimir effect at zero temperature is always attractive. However, at finite temperature, a repulsive Casimir effect can emerge from a critical temperature. I. INTRODUCTIONThe Casimir effect is a quantum remarkable phenomenon with numerous applications. This effect was first proposed by H. Casimir, in 1948 [1]. It describes an attractive force that arises between two parallel conducting plates placed in the vacuum of a quantum field. About ten years after the theoretical proposal, experimental confirmation was carried out [2]. Recently, the experimental accuracy has increased significantly [3][4][5][6][7]. The original idea was developed using the electromagnetic field. However, nowadays this phenomenon appears in any quantum field. The Casimir effect emerges when boundary conditions or topological effects are imposed on a quantum field. As a consequence, the vacuum energy of the field is modified [8][9][10]. In this paper, the quantum field to be considered is the massless scalar field coupled to gravity. In this context, thermal effects are investigated having as a gravitational background the Gödel-type solutions.Temperature changes the properties and behavior of any system. Furthermore, phenomena at zero temperature generally do not occur in nature. To be more realistic let us introduce the